let 'x' and 'y' be the two numbers

the arithmetic mean of 2 numbers is 20 means

(x + y)/2 = 20

x + y = 40

y = 40 - x

their standard deviation is 5

(1/2)((x - 20)^2 + (y - 20)^2) = 5^2

(x - 20)^2 + (y - 20)^2 = 50

plug y = 40 - x into the last equations

(x - 20)^2 + ((40 - x) - 20)^2 = 50

by solving we find two roots

x1 = 25

x2 = 15

click here to see the step by step solution of the quadratic equation

for x = 25 we have y = 40 - 25 = 15

for x = 15 we have y = 40 - 15 = 25

the two numbers are 15 and 25.